# C4 differential equation

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Thread starter 3 years ago
#1
Water is pouring into a bucket at a constant rate of 30cm^2 per second and is leaking out at a rate proportional to the volume of water already in the bucket.

1) show that at time t seconds the volume Vcm^2 of water in the bucket satisfies the differential equation dv/dt =30-kv where k is a positive constant

The bucket is initially empty
2) solve the differential equation and show that V=A +Be^-kt giving the values of A and B in terms of k.
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3 years ago
#2
(Original post by cassidy11)
Water is pouring into a bucket at a constant rate of 30cm^2 per second and is leaking out at a rate proportional to the volume of water already in the bucket.

1) show that at time t seconds the volume Vcm^2 of water in the bucket satisfies the differential equation dv/dt =30-kv where k is a positive constant

The bucket is initially empty
2) solve the differential equation and show that V=A +Be^-kt giving the values of A and B in terms of k.
What have you tried? Also your volume dimensions are slightly off...
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Thread starter 3 years ago
#3
(Original post by RDKGames)
What have you tried?
I honestly don't know where to start i set t as 0 but didn't know where to go then
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Thread starter 3 years ago
#4
(Original post by RDKGames)
What have you tried? Also your volume dimensions are slightly off...
I know I was just thinking that lol but that's what the question says
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3 years ago
#5
(Original post by cassidy11)
I honestly don't know where to start i set t as 0 but didn't know where to go then
Okay so formulate the information given.

is your change of volume

You have going in

Then you have some going out, denote this as and we know where

So your change of volume at each instant of time is defined by how much is going in take away the amount that is going out.

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Thread starter 3 years ago
#6
(Original post by RDKGames)
Okay so formulate the information given.

is your change of volume

You have going in

Then you have some going out, denote this as and we know where

So your change of volume at each instant of time is defined by how much is going in take away the amount that is going out.

Thank you very much do you know how to solve it?
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3 years ago
#7
(Original post by cassidy11)
Thank you very much do you know how to solve it?
It's a seperable first order linear differential equation: you should know how to solve it.
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